Expression of type ExprTuple

from the theory of proveit.linear_algebra.tensors

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, ExprTuple, K, Lambda, V, n
from proveit.linear_algebra import TensorExp, VecSpaces
from proveit.logic import CartExp, Forall, InSet, SubsetEq
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(n, Conditional(Forall(instance_param_or_params = [V], instance_expr = SubsetEq(TensorExp(V, n), CartExp(V, n)), domain = VecSpaces(K)), InSet(n, NaturalPos))))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(n \mapsto \left\{\forall_{V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\left(V^{\otimes n} \subseteq V^{n}\right) \textrm{ if } n \in \mathbb{N}^+\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 29 body: 3
2	ExprTuple	29
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	29, 11
10	Lambda	parameter: 28 body: 13
11	Literal
12	ExprTuple	28
13	Conditional	value: 14 condition: 15
14	Operation	operator: 16 operands: 17
15	Operation	operator: 18 operands: 19
16	Literal
17	ExprTuple	20, 21
18	Literal
19	ExprTuple	28, 22
20	Operation	operator: 23 operands: 25
21	Operation	operator: 24 operands: 25
22	Operation	operator: 26 operand: 30
23	Literal
24	Literal
25	ExprTuple	28, 29
26	Literal
27	ExprTuple	30
28	Variable
29	Variable
30	Variable